Asymptotic linking of volume-preserving actions of ${\mathbb{R}}^k$

Abstract

We extend V. Arnold's theory of asymptotic linking for two volume preserving flows on a domain in ${\mathbb{R}}^3$ and $S^3$ to volume preserving actions of ${\mathbb{R}}^k$ and ${\mathbb{R}}^{\ell }$ on certain domains in ${\mathbb{R}}^n$ and also to linking of a volume preserving action of ${\mathbb{R}}^k$ with a closed oriented singular $\ell$-dimensional submanifold in ${\mathbb{R}}^n$, where $n=k+\ell +1$. We also extend the Biot-Savart formula to higher dimensions.

33 pages. We extend Arnol'd's asymptotic linking to actions of ${\mathbb^R}^k$ and ${\mathbb^R}^\ell$. Some typographical errors were corrected and references to Schwartzman's asymptotic cycles were added

References in corpus (1)

• Link Invariants for Flows in Higher Dimensions